Existence and decay of solutions to the dissipative quasi-geostrophic equation with delays

We consider the dissipative quasi-geostrophic equation with forcing and advective terms containing delays. We prove the existence of weak solutions and algebraic decay of the energy, provided the initial data θ0θ0 is in Lp∩L2,1≤p<2Lp∩L2,1≤p<2 and the forcing term satisfies some mild conditions on its long time behavior.